Mathematical Modeling of the Pituitary-Thyroid Feedback Loop: Role of a TSH-T₃-Shunt and Sensitivity Analysis

Despite significant progress in assay technology, diagnosis of functional thyroid disorders may still be a challenge, as illustrated by the vague upper limit of the reference range for serum thyrotropin (TSH). Diagnostical problems also apply to subjects affected by syndrome T, i.e., those 10% of hypothyroid patients who continue to suffer from poor quality of life despite normal TSH concentrations under substitution therapy with levothyroxine (L-T₄). In this paper, we extend a mathematical model of the pituitary-thyroid feedback loop in order to improve the understanding of thyroid hormone homeostasis. In particular, we incorporate a TSH-T₃-shunt inside the thyroid, whose existence has recently been demonstrated in several clinical studies. The resulting extended model shows good accordance with various clinical observations, such as a circadian rhythm in free peripheral triiodothyronine (FT₃). Furthermore, we perform a sensitivity analysis of the derived model, revealing the dependence of TSH and hormone concentrations on different system parameters. The results have implications for clinical interpretation of thyroid tests, e.g., in the differential diagnosis of subclinical hypothyroidism.